Ok.... Here's the scoop.
If you have a Cobra you can race SCCA with GT-1. There are some real significant limitations when it comes to engine configurations and you are limited to 16" wheels, but you can run slicks. Your Cobra will not be competitive, but you can have fun. This is SCCA's only appropriate national class for the Cobra. Most GT-1 cars are former Trans-Am cars that go like stink.
At a regional level, you can run ITE or SP, depending on your region. Note that these classes don't let you at the Valvoline Run-Offs, but it doesn't matter since you wouldn't be competitive here either. ITE is usually the Vipers and hot shot BMWs that are only slightly slower than the GT-1 cars. SP varies more across the country, but often includes the cars that *couldn't* qualify for GT-1. So these cars can be wicked fast. I've seen SP cars that easily cost $250K.
If you run an FFR Spec Cobra, you can run in the Spec Roadster series with NASA. NASA has strong chapters on the west coast, mid-altantic (Virginia chapter), Florida, Ohio/Indiana, Arizona, and now Texas/Oklahoma. In the northeast, they are running with COM, but this is a time trial on road course - not wheel to wheel racing.
If you have a Superformance, ERA, or FFR car not built to the Spec Racer rules, you can run with NASA in what is called SU-1. This is basically the unlimited categor and features very fast cars. Dennis Olthoff brought his beautiful One Lap car and did very well, but it sort of depends on who shows up. I have seen a Nissan Sentra run in SU and I have seen a Jaguar 220 (yep. Gorgeous) also in there. I don't know what you would have to do to run in something like SU-2, but my guess it would involve less horsepower and an ugly car.
www.scca.org has some info, but it isn't great. You can try sccaforums.com
www.nasaproracing.com has more info on the classes. The Virginia region has an outstanding forum that can answer many of your questions very quickly:
http://www.nasaracing.net/pHP_BB/phpbb2/index.php
Hope that helps!
-Dan